# load weather and game data for Boston boston_game_weather <-read_csv(bos_game_weather_html)# create separate columns with day, month, and year corresponding# to game dates; and create a binary win (1) or not (0) columnboston_game_weather <- boston_game_weather %>%mutate(year=year(date),month=month(date),day=day(date),wl_binary=ifelse(wl=="W",1,0))# load sports venue datapro_sports_venues <-read_csv(venues_html)# extract baseball parksbaseball_parks <- pro_sports_venues %>%filter(Sport =="MLB")# add info about open roofbaseball_parks$Open_Roof <-c("No",rep("Yes",9),"No","Yes","Yes","Yes","No","No",rep("Yes",7),"No","Yes","Yes","No","No","No","Yes")# load map data for US states minus AK and HIstates_df <-map_data("state") %>%filter(region !="alaska"| region !="hawaii")
Executive Summary
In this project we explore the impact that weather conditions may have on Major League Baseball (MLB) teams that play in open-air stadiums. We take as a case study the Boston Red Sox and their home stadium Fenway Park. Through inferential and predictive models, we find lack of evidence that weather conditions have a significant impact on team performance or game outcome. We do find evidence that weather conditions may have an impact on game attendance. Additionally, we examine factors that may impact game duration and find that weather conditions do not appear to have a significant impact on game duration. However, there is evidence that the number of runs scored by the home team and visiting team may have an impact on game duration. As a consequence of our modeling, we are able to quantify the impact that the number of runs scored by a visiting team has on the likelihood for the Red Sox to win a game.
Figure 1: The 30 MLB park locations and their open-air status. Darker shading indicates overlap of nearby parks.
Initial Research Question
We would like to know about the impact that climate or weather may have on MLB teams that play in open-air stadiums. Given that climate and weather patterns are changing and impacting many aspects of our society and lives, and given that many MLB parks are exposed to the elements for many months of the year, it could be that changing climate and weather conditions may impact MLB. In particular, we would like to know if changing climate and weather patterns might have an effect on either team performance or game attendance.
Figure 3: MLB park locations and open-air status with Fenway Park in Boston, MA highlighted.
The main part of this project combines data about home games played at Fenway Park with historical Boston area weather data in an attempt to assess if changing climate and weather conditions have impacted either team performance or game attendance at Fenway, with Fenway serving as an example of an open-air baseball stadium.
Data Collection and Documentation
To address our primary question, we collected and combined two sets of data. The first data set collected contains information about each home game played by the Boston Red Sox at Fenway Park. The second data set collected contains weather data such as in Boston over the available time frame of games at Fenway.
Team Data
To obtain the data on home games played by the Boston Red Sox at Fenway Park, we used the function get_retrosheet from the R package retrosheet to download game data for a specific year and team (Douglas and Scriven 2023). Then, we used a function team_games to iterate over all the years that the Red Sox played at Fenway Park, that is, 1912 - 2022 (skipping 2020 due to the COVID-19 pandemic). The code to accomplish this is in the team_home.R script available at our baseball_weather GitHub repository, view the GitHub repo.
The retrosheet package contains a collection of tools to import and structure the single-season event, game-log, roster, and schedule data available from the Retrosheet website which maintains play-by-play accounts of as many major league games as possible. The Retrosheet data we downloaded for the Boston Red Sox has a structure indicated by Table 1.
Table 1: A few rows of the Retrosheet data downloaded for the Boston Red Sox home games at Fenway Park.
date
dbl_hdr
hm_tm
vis_runs
hm_runs
attendance
duration
score_diff
wl
1912-04-20
0
BOS
6
7
24000
190
1
W
1912-04-23
0
BOS
6
2
2500
145
-4
NW
1912-04-24
0
BOS
5
2
2500
135
-3
NW
1912-04-25
0
BOS
1
4
3000
118
3
W
1912-04-26
0
BOS
6
7
10000
125
1
W
Each row corresponds to a single home game at Fenway. The columns of the data set specify for each game the date, whether the game is a double-header, the number of runs scored by the home team (Boston), the number of runs scored by the visiting team, the game attendance, the duration of the game in minutes, the difference between the home team score and the visiting team score, and whether Boston won (W) or did not win (NW).
The data set contains 8,634 rows or observations.
Weather Data
We used R package RNCEP to download climate and weather data for the Boston area (Kanamitsu 2002). This package simplifies the access, organization, and visualization of weather data from the NCEP/NCAR reanalysis and NCEP/DOE reanalysis II data sets. Specifically, we used the function NCEP.gather.surface to download data for the surface temperature (air.sig995), precipitation (rhum.sig995), and humidity (pr_wtr.eatm). See the documentation for RNCEP for more details and specifications of units used. The climate and weather data we downloaded for Boston has a structure indicated by Table 2.
Table 2: A few rows of the climate and weather data downloaded for Boston.
tempK
humid
precip
date
276.3125
63.3750
5.668751
1950-04-01
280.3000
81.0625
12.656252
1950-04-02
281.2875
79.4375
15.000000
1950-04-03
285.2188
92.1250
24.950001
1950-04-04
285.9813
93.6875
27.612501
1950-04-05
The data set contains 15,622 rows or observations. Note that the temperature, humidity, and precipitation values recorded are averaged daily and over a spatial region (between 41 and 42 degrees latitude and 289 and 290 degrees longitude). The code used to download the data is contained in the boston_weather_get.R script available our baseball_weather GitHub repository, view the GitHub repo.
Combined Weather and Game Data
In order to address our initial research question, we combined the Boston weather and home game data. It is important to emphasize the following:
Climate and weather data is only available starting in the 1950’s while Boston Red Sox home grame data goes back to 1912. Thus, we must restrict the home game data to those observations starting in the 1950’s.
The downloaded climate and weather data contains observations for many more days than just the days on which there were Red Sox home games. Thus, we must extract those climate and weather observations corresponding to dates of games at Fenway.
The combined weather game data for the Boston Red Sox home games at Fenway Park has a structure indicated by Table 3.
Code
boston_game_weather %>%head(5) %>%kable()
Table 3: A few rows of the weather and game data for the Boston Red Sox home games at Fenway Park.
date
dbl_hdr
hm_tm
vis_runs
hm_runs
attendance
duration
score_diff
wl
tempK
humid
precip
tempF
year
month
day
wl_binary
1950-04-18
0
BOS
15
10
31822
208
-5
NW
284.8500
80.2500
18.29375
53.06000
1950
4
18
0
1950-04-19
1
BOS
3
6
25425
150
3
W
284.8813
85.9375
17.17500
53.11625
1950
4
19
1
1950-04-19
2
BOS
16
7
32860
190
-9
NW
284.8813
85.9375
17.17500
53.11625
1950
4
19
0
1950-04-28
0
BOS
1
4
5333
116
3
W
282.8500
90.5625
19.40625
49.46001
1950
4
28
1
1950-04-30
1
BOS
0
19
0
131
19
W
280.4438
85.3125
21.54375
45.12876
1950
4
30
1
This is our principal data set and it contains 5,727 rows.
Exploratory Analysis and Results
The script boston_home_weather_eda.R contains the full exploratory analysis and all corresponding code.
Potential Response Variables
Figure 4 shows the distributions of runs scored by the Red Sox and the visiting team, as well as the number of games and the difference in scores between the Red Sox and visiting teams. The median number of runs for Boston is 5 while the median number of runs for visitors is 4.
Code
ra_1 <- boston_game_weather %>%ggplot(aes(x=hm_runs)) +geom_histogram(color="#512d6d",fill="lightblue") +xlab("Number of Runs by Boston") +ylab("Count")# Number of visitor runsra_2 <- boston_game_weather %>%ggplot(aes(x=vis_runs)) +geom_histogram(color="#512d6d",fill="lightblue") +xlab("Number of Runs by Visitors") +ylab("Count")# Boston runs - Visitor runsra_3 <- boston_game_weather %>%ggplot(aes(x=score_diff,fill=wl)) +geom_histogram(color="#512d6d") +scale_fill_manual(values =c("#E69F00","#009E73")) +labs(x ="Boston Runs - Visitor Runs",y ="Count",fill="Win/Not")# Win or Not Winra_4 <- boston_game_weather %>%ggplot(aes(x=wl,fill=wl)) +geom_bar(color="#512d6d") +scale_fill_manual(values =c("#E69F00","#009E73")) +theme(legend.position ="none") +labs(x ="No Win or Win",y ="Count")(ra_1 + ra_2) / (ra_4 + ra_3)
Figure 4: Exploratory plots for the distributions of Red Sox runs, visitor runs, score difference, and wins for Red Sox home games played at Fenway Park from 1950 to 2022 (excluding 2020).
We observe from Figure 4 that the Red Sox have won more games than they have lost and tend to win by a median of one run.
Figure 5 displays the distributions for the duration and attendance of Red Sox home games played at Fenway Park from 1950 to 2022 (excluding 2020). The median duration for a game is 170 minutes while the median attendance is around thirty thousand. Note that Fenway Park currently seats over 37,000 people (“Fenway Park - Wikipedia — En.wikipedia.org”).
Figure 5: Exploratory plots for the distributions of game duration and attendance and Red Sox home games played at Fenway Park from 1950 to 2022 (excluding 2020).
One potentially important observation based on Figure 5 is that there are some Red Sox home games for which the recorded attendance is 0. Specifically, there are 243 such games. This value is determined using the following code:
boston_game_weather %>%filter(attendance ==0) %>%ggplot(aes(x=year)) +geom_bar(color="#512d6d",fill="lightblue") +labs(x="Year",y="Count",title="Observations with Zero Recorded Attendance")
Figure 6: The number of Red Sox home games by year with a recorded attendance of zero.
It’s not immediately clear why there may be a zero recorded for attendance at some games. This could be an error but further investigation is required to determine for certain. It might be necessary to remove those observations with zero attendance depending on what specific questions we decide to address with models. Furthermore, due to the skewness of the attendance distribution, it may be useful to transform the attendance variable in order to facilitate modeling.
Potential Predictor Variables
Our main interest in this project is to examine how climate and weather factors impact aspects of baseball games such as the score, outcome, duration, and game attendance. As previously noted, we have data about humidity, precipitable water2, and temperature for the Red Sox home games.
Climate and Weather Variables
Figure 7 show the distributions for humidity (as a percent), temperature (in degrees Fahrenheit), and precipitable water (in units of \(\frac{\text{kg}}{\text{m}^2}\)).
Figure 7: Exploratory plots for the climate and weather variables on dates of Red Sox home games played at Fenway Park from 1950 to 2022 (excluding 2020).
We see that the median temperature is about 65 degrees Fahrenheit, the median humidity is about 83 percent, and the median precipitable water is about 25 \(\frac{\text{kg}}{\text{m}^2}\).
Variable Relationships
We would like to determine what if any impact there has been on the score, outcome, duration, or attendance of Red Sox games over time by temperature, humidity, or precipitable water.
Figure 8 shows the number of runs scored by the Boston Red Sox at each home game from 1950 to 2022 (2020 excluded) plotted against date, temperature, humidity, and precipitable water, respectively.
Figure 8: The number of runs scored by Red Sox at home games at Fenway Park plotted against the game date, and climate and weather variables.
Here it is difficult to see any clear pattern of influence that date, temperature, humidity, or precipitable water have on the number of runs the Red Sox score at home games over the specified period of time. We observe that there are potential outliers in each of the plots in Figure 8.
Figure 9 shows the wins for the Boston Red Sox at each home game from 1950 to 2022 (2020 excluded) plotted against date, temperature, humidity, and precipitable water, respectively.
Figure 9: The wins by Red Sox at home games at Fenway Park plotted against the game date, and climate and weather variables.
Again, it is difficult to see any clear pattern of influence that date, temperature, humidity, or precipitable water have on whether the Red Sox win at home games over the specified period of time.
Figure 10 shows the duration of games for the Boston Red Sox at each home game from 1950 to 2022 (2020 excluded) plotted against date, temperature, humidity, and precipitable water, respectively.
Figure 10: The game duration for Red Sox home games at Fenway Park plotted against the game date, and climate and weather variables.
We clearly see that the duration of games has generally increased from 1950 to 2022. However, it is difficult to see any clear pattern of influence that temperature, humidity, or precipitable water have on whether the duration of Red Sox home games.
Figure 11 shows the attendance of games for the Boston Red Sox at each home game from 1950 to 2022 (2020 excluded) plotted against date, temperature, humidity, and precipitable water, respectively.
Figure 11: The game attendance for Red Sox home games at Fenway Park plotted against the game date, and climate and weather variables.
We clearly see that the attendance of games has generally increased from 1950 to 2022. Further, it also appears that attendance increases with temperature, humidity, and precipitable water. Some additional points include:
It appears that over time, the variance of game attendance has decreased, and there is a period of time (roughly 2005-2010) that the variance of game attendance is very low relative to other years. It is potentially interesting to determine a potential cause for this since it suggests that the Red Sox games where consistently well-attended during that time.
While attendance appears to increase with increasing temperature, humidity, and precipitable water it is unlikely that an increase in temperature, humidity, or precipitable water causes more people to attend Red Sox home games. For example, attendance might be increasing over time for any number of reasons and perhaps temperature, humidity, and precipitable water are increasing with time. Further exploratory analysis might provide insight on this.
Further Exploratory Analysis
Figure 12 shows the average number of home game wins per year for the Red Sox.
Code
boston_game_weather %>%group_by(year) %>%summarise(wins_by_year=sum(wl_binary)) %>%ggplot(aes(x=year,y=wins_by_year)) +geom_point(size=2,color="darkgreen") +geom_smooth(color="#512d6d",fill="lightblue") +labs(x="Year",y="Number of Wins")
Figure 12: The number of home games at Fenway Park which the Red Sox won plotted against year.
We observe that from around 2003 to 2009, the Red Sox where consistently winning a large number of games. This could relate to our earlier observation regarding the time period of consistently high game attendance observed in Figure 11.
Since the number of home games might vary across years, we also plot the proportion of home games won by the Red Sox per year in Figure 13.
Figure 13: The proportion of home games at Fenway Park which the Red Sox won plotted against year.
This shows that the Red Sox tend to win around 60% of their home games. However, we also see that the Red Sox won a higher proportion of their home games from around 2003 to 2009.
Figure 14 shows the change in the both the daily and yearly average climate and weather variables over time.
Figure 14: Plots showing the change in the climate and weather variables over time.
It appears that there may be some temporal trends in the climate and weather variables over time. In order to explore more about how the climate and weather over time may have an impact on the score, outcome, duration, or attendance of Red Sox home games, we will need to develop an appropriate modeling approach and assess it’s performance.
Models
We will use different models to address several different questions. First, we will use logistic regression to assess whether there is a relationship between the climate and weather variables, time, and visiting team performance and the outcome of the game (win or loss). Second, we will use linear regression to assess whether there is a relationship between the climate and weather variables, time, and visiting team performance and the number of runs scored by Boston. Finally, we will use decision trees to build predictive models for the duration and attendance of games.
For the first two models, we use the bootstrap in order to estimate the sampling distributions and confidence intervals for the model coefficients. For the decision tree models, we use cross-validation to tune hyperparameters and estimate the predictive accuracy of the models.
Model Results
Predictors of Wins
Figure 15 shows the bootstrap estimates for the logistic regression coefficients for the predictors of win/loss along with estimates for the 95% confidence intervals. Since the confidence intervals for date, humididty, precipitation, and temperature all include 0, we cannot conclude that there is a relationship between these variables and the outcome of the game. However, we do observe that there is evidence that a visiting team’s performance is negatively associated with the probability of a win for the Red Sox. While this is not a surprising result, it provides us with a quantitative estimate of the impact of the visiting team’s performance on the outcome of the game.
Figure 15: Bootstrap estimates for logistic regression coefficients for win/loss.
Figure 16 shows a series of bootstrap predictions for the probability of a win for the Red Sox as a function of the visiting team’s performance. We observe that as the visiting team’s performance increases, the probability of a win for the Red Sox decreases. The observed data is plotted along with the model predictions.
Figure 16: Bootstrap predictions for logistic regression model for win/loss plotted against the number of runs scored by a visiting team.
Predictors of Runs Scored
Figure 17 shows the bootstrap estimates for the linear regression coefficients for the predictors of number of runs scored by the Red Sox along with estimates for the 95% confidence intervals. Since the confidence intervals for humidity, precipitation, and temperature all include 0, we cannot conclude that there is a relationship between these variables and the number of runs. The model does provide evidence that the number of runs scored by the Red Sox has increased over time, and that the visiting team’s performance is positively associated with the number of runs scored by the Red Sox. However, in both cases the effect size is quite small.
Figure 17: Bootstrap estimates for linear regression coefficients for number of runs scored by Red Sox.
Game Attendance Model Results
To examine influences on game attendance, we start with a linear regression model with the log of attendance as the response variable and the climate and weather variables, time, and visiting team performance as the predictor variables. We use the bootstrap to estimate the sampling distributions and confidence intervals for the model coefficients. The results are shown in Figure 18. We observe that the confidence intervals for the coefficients for date, humidity, precipitation, and temperature all exclude 0. Thus, there is evidence of a relationship between these variables and the attendance of the games. Specifically, evidence suggests that there is a slight decrease in game attendance corresponding to an increase in precipitation. On the other hand, there is a slight to moderate increase in game attendance corresponding to an increase in temperature and humidity. Finally, there is evidence of increased in game attendance over time.
Figure 18: Bootstrap estimates for linear regression coefficients for game attendance.
To go further, we also build a predictive model by tuning a decision tree to predict game attendance based on the predictors used in the linear regression model. We use cross-validation to tune the hyperparameters and estimate the predictive accuracy of the model. The results are shown in Figure 19 and Figure 20. We observe that the most important predictors for the model are the date and temperature. This is consistent with our findings from the linear regression model. The model predictions are plotted against the observed values in Figure 20. We observe that the model does a reasonable job of predicting the game attendance.
Figure 19: Variable importance measures for predictors in tuned decision tree model for the game attendance.
Figure 20: Predicted values versus observed values for tuned decision tree model for game attendance.
Note that the predictive accuracy of the model seems to be better in later years.
Table 4 records the values of test error metrics used to assess the performance of the tuned decision tree model for game attendance.
Table 4: Metrics to assess model perforamnce for tuned decision tree to predict game attendance.
Metric
Value
rmse
0.1709739
rsq
0.5375165
mae
0.0987486
Based on the test error metrics, we conclude that this model is mediocre with regard to its predictive accuracy although its qualitative results are consistent with those of our linear regression analysis.
Game Duration Model Results
Similar to our analysis for game attendance, we start with a linear regression model with the game duration as the response variable and the climate and weather variables, time, and visiting team performance as the predictor variables. We use the bootstrap to estimate the sampling distributions and confidence intervals for the model coefficients. The results are shown in Figure 21. We observe that the confidence intervals for the coefficients for humidity, precipitation, and temperature all include 0 while the confidence intervals for the coefficients for Red Sox win, visitor runs, Red Sox runs, and date all exclude 0. Thus, evidence suggests that games are shorter when the Red Sox win, but overall longer when more runs are scored by either team. Further, there is evidence that games have gotten longer over time.
Figure 21: Bootstrap estimates for linear regression coefficients for game duration.
The results of the tuned decision tree model for game duration are shown in Figure 22 and Figure 23. We observe that the most important predictors for the model are the date and the number of runs scored by each team. The model predictions are plotted against the observed values in Figure 23. We observe that the model does a reasonable job of predicting the game duration except when the games are particularly long.
Figure 22: Variable importance measures for predictors in tuned decision tree model for the game duration.
Figure 23: Predicted values versus observed values for tuned decision tree model for game duration.
Table 5: Metrics to assess model perforamnce for tuned decision tree to predict game duration.
Wickham, Hadley, Romain François, Lionel Henry, Kirill Müller, and Davis Vaughan. 2023. Dplyr: A Grammar of Data Manipulation. https://CRAN.R-project.org/package=dplyr.
By “open-air” we mean permanently open with no option for roof cover. Stadiums with either a fixed or retractable roof are not considered to be open-air for our purposes.↩︎
Precipitable water is the amount of water potentially available in the atmosphere for precipitation, usually measured in a vertical column that extends from the Earth’s surface to the upper edge of the troposphere.↩︎
